Just off the top of my head and not being anything like an educational scholar or anything, but I don't think it would be advantageous or ethical to do that. Number one, I don't think we can reliably type children (not sure we can reliably type anyone, actually- it's always going to be a rough guess). Number two, different personalities have different things to offer in an educational setting- it's not, or it shouldn't be, kids sitting there soaking up information from an authority figure. They participate in their own education and help each other in various ways. We need balance to expose students to all kinds of perspectives. Number three, as an NF many of my favorite people are NTs and I also love me some SJs and SPs, and it would have sucked to have been stuck with all my own "kind" so to speak. I think we all do best when there's a give-and-take and some air in the system. It's that many perspectives thing.
All of the above would go for Socionics quadrants as well, I assume, though I don't know as much about those.
That makes sense, I was thinking that possibly grouping them together with their peers would help them learn in an environment engineered to their type. Today's schools are built for SJs and all of the students (especially NTs) are taught to become more like them, it's quite sad.
The Socionics Quadrant would be interesting however, because it pairs 4 types that work well together and often make friends with each other.
For Example:
(Remember that the introverted types get screwed up when making the transition, the most common of which being that INTPs in MBTI mostly become LII INTjs, and INTJs in MBTI mostly become ILI INTps)
Alpha Quadrant - ENTp (LIE), INTj (LII/MBTI INTP), ISFp (SEI), ESFj (ESE)
Beta Quadrant - ENFj (EIE), ISTj (LSI), ESTp (SLE), INFp (IEI/MBTI INFJ?)
Gamma Quadrant - ESFp (SEE), INTp (ILI/MBTI INTJ), ENTj (LIE), ISFj (ESI)
Delta Quadrant - ESTj (LSE), INFj (EII/MBTI INFP?), ENFp (IEE), ISTP (SLI)
http://www.socionics.us/theory/quadras.shtml